(a): gravitational lensing
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24/9/2010 1
Les gens ont des étoiles qui ne sont pas les mêmes.
Pour les uns qui voyagent, elles sont des guides.
Pour les autres, elles ne sont rien que des petites lumières.
Pour d’autres, qui sont savants, elles sont des problèmes.
Le Petit Prince (Antoine de St Exupéry)
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(A): Gravitational lensing (B): Optical lens experiment
Deflector plane Observer plane Observer planeLens plane
O1 O1
O2 O2
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(A): Gravitational lensing (B): Optical lens experiment
Deflector plane Observer plane Observer planeLens plane
O1 O1
O2 O2
24/9/2010 4
(A): Gravitational lensing (B): Optical lens experiment
Deflector plane Observer plane Observer planeLens plane
O1 O1
O2 O2
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r
ni
ε(ξ)
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2. Gravitational lenses5. THE OPTICAL GRAVITATIONAL LENS (GL)
EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:
Deflection of a light ray passing through an axi-ally symmetric optical lens.
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2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:
, (5.1)
, (5.2)
, (5.3)
, (5.4)
. (5.5)
r
irin
sinsin
rGMric
2
)(4)(
rdd
cnGM
dd
2)1()(4
00
2ln
1sc
nR
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2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:
Right: examples of (upper left) a 'point mass' lens (28 cm in diameter) manufactured at the Hamburg Observatory and of (lower right) a 'spiral galaxy' optical lens (30 cm in diameter) produced by the authors at the European Southern Observatory (Garching bei München).
Below: several examples of axially symmetric optical lensessimulating the light deflection properties due to a point mass(a), a SIS galaxy (b), a spiral galaxy (c), a uniform disk (d)and a truncated uniform disk of matter (e).
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2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:
d / d = -K, (5.6)
() = (0) + K (0 - ). (5.7)
(5.8)
, (5.9)
, (5.10)
0
2 ' ' 'M d
2
02 1 exp / 1/c cc
M
0 exp / c
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2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:
, (5.11)
M() = 0 2, if c, (5.12a)
M() = 0 c2, if c. (5.12b)
0
2/0 0 0
20 /
8 exp( )ln exp exp( 1)
c
c
c
c c
G z dzzn c
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2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:
if c 0, (5.13a)
(5.13b)
if c. (5.13c)
20 020
4ln
( 1) c
G
n c
20 020
4ln
( 1)c cc
G
n c
2 202
2( )
( 1)c c
G
n c
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GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)
= 4GM / (c2 x)
x
y = y0 + K (x02 – x2), with K = 1/(2 Rsc)
y
dy/dx = -tg(r) with i + r + = π, i = r, and thus r = π/2 - /2and finally,
r i
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GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)
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GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)
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= 4GM / (c2 x)
x
y = y0 + K ln(x0 / x) with K = Rsc)
y
GL mirage simulator for the case of normal incidence light reflection
(point- like mass lens)
dy/dx = -r with i + r = , i = r, and thus r = /2and finally,
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GL mirage simulator for the case of normal incidence light reflection
(point- like mass lens)
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GL mirage simulator for the case of normal incidence light reflection
(point- like mass lens)
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GL mirage simulator for the case of grazing incidence light reflection (uniform disk lens)
y = y0 + K ln(x0 / x), with K = c2/(2GπΣ0)
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GL mirage simulator for the case of normal incidence light reflection (uniform disk lens)
y = y0 + K (x02 – x2) with K = (4G/c2)πΣ0
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The Optical GL Experiment (light relection)
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THE OPTICAL GL EXPERIMENT:
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THE OPTICAL GL EXPERIMENT:
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THE OPTICAL GL EXPERIMENT:
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